What the two orders actually change
Every month you pay all the minimums plus one shared extra budget. The snowball aims that extra at the smallest balance, the avalanche at the highest APR. Once a debt is cleared, its minimum rolls onto the next one, so the payoff accelerates either way - the only difference is which balance disappears first, and therefore whose interest stops first.
Because the avalanche kills the most expensive debt first, it generally accrues less total interest. But the snowball clears a debt sooner, and that early win is the psychological engine that keeps people paying through a multi-year plan. The page prices that trade-off in dollars, on your actual balances, instead of leaving it as a slogan.